category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
monoidal dagger-category?
homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
n-category = (n,n)-category
n-groupoid = (n,0)-category
The coherence theorem for braided monoidal categories can be expressed as:
Every diagram in a free braided monoidal category made up of associators and unitors and braidings?, and in which both sides have the same underlying braid?, commutes.